Problem: $f(x) = \dfrac{ x + 8 }{ ( x + 8 )( x - 3 ) }$ What is the domain of the real-valued function $f(x)$ ?
Answer: $f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-8$ or $x=3$ So we know that $x \neq -8$ and $x \neq 3$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-8, \,x \neq3\, \}$.